Grinding or milling of tools having a square cross-section (such as for example tap drills) require a clamping arrangement which centrally clamps the portion of the tool having the square cross-section. Such clamping arrangements have, because of their complex construction, a relatively large diameter and can only be used in machines where the grinding disc or milling tool is mounted during operation transversely to the central axis of the tool. In those operations where the grinding wheel is arranged in the same direction as the central axis of the tool such as, for example when slots or grooves are to be ground along the longitudinal axis of the machine, the known clamping arrangements can not be used because the longitudinal groove or slot must generally extend up to the portion having the square cross-section and the grinding wheel would therefore cut into the chuck if the chuck exceeds a certain diameter. For this reason the grinding machines and milling machines of the state of the art have chucks which have four-sided pyramidically shaped bores (that is the bore has a square cross-section) and wherein the four sides of the pyramidically shaped bore converge inwardly so that they may clampingly hold the portion of the tool having a square cross-section which is inserted therein. This type of clamping arrangement has the drawback that, when the portion of the tool with the square cross-section has not been grindingly accurately squared, the tool will not be precisely axially clamped in the chuck.